Question

Darryl Dixon shoots an arrow at a zombie. The path of the arrow can be modeled with the equation y=-x^2 42x-80, where x is time in seconds and y is the height in feet. How long does it take for the arrow to reach its maximum?

Answer 1

We need to find time taken to reach arrow to its maximum.

The path of the arrow can be modeled with the equation $y=-x^2+ 42x-80$ .

Differentiating the given equation w.r.t x and equate it to zero.

$\dfrac{dy}{dx}=-2x + 42 \\\\42 - 2x = 0\\\\x = 21\ seconds$

Putting value of x = 21 sec in given equation, we get :

$y=-x^2+ 42x-80\\\\y = -(21)^2 + (42\times 21) - 80\\\\y = 361 \ feet$

Therefore, time taken to reach maximum height is 21 seconds.